# Solving inequalities

Concept

Solving for the unknown variable in inequalities is by no means an easy feat for a young child. This is especially so for someone who is just starting out in learning algebra. In most situations, *solving inequalities* would be split into two types: linear inequalities and quadratic inequalities. We shall begin with the easier type of inequality, linear inequality. Those who are already familiarized with linear inequality should proceed with quadratic inequalities.

Linear inequality questions normally ask students to find the unknown range. For instance, the question asks to find the range of values that satisfy the inequality 5- x bigger than 3. After some rearranging of numbers, we can determine that x smaller than 2.

If we were to draw this out,

The answer is x smaller than 2.

Sometimes, solving linear inequality can be tricky when there are two linear inequalities. At that point, you have to consider the terms ( **and ** , **or **) surrounding the inequalities.

Example

Illustrate on the number line, the range of values of y which satisfy
and

and

and

In this example, you are looking at a range of values of y that satisfy both inequalities.

This is a relatively simple question which simply requires the student to understand the implications of having more than one restriction on a particular solution set.

If the question was phrased as**or** ,

then the answer would be all real numbers since any real number would satisfy either inequality.

Reminder: You have to carefully look at the question and find which term ( and, or) was used. This lets you decide which of the solutions satisfy the requirements of the question

'Try it out Yourself' Section

Find the range of values of x for the following inequalities and illustrate with a number line.

a)

b) and

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